A complex function f is said to have an isolated singularity at a point z if it fails to be analytic at z, but there exists a neighbourhood of z on which f is analytic everywhere but z. (In other words, f is analytic on some punctured disk centred at z, but not at z.) For example, the function 1 / (z2+4) has isolated singularities at 2i and -2i.

Isolated singularities are further classified as removable singularities, poles or essential singularities.

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